A Non-Sequential Representation of Sequential Data for Churn Prediction

We investigate the length of event sequence giving best predictions when using a continuous HMM approach to churn prediction from sequential data. Motivated by observations that predictions based on only the few most recent events seem to be the most accurate, a non-sequential dataset is constructed from customer event histories by averaging features of the last few events. A simple K-nearest neighbor algorithm on this dataset is found to give significantly improved performance. It is quite intuitive to think that most people will react only to events in the fairly recent past. Events related to telecommunications occurring months or years ago are unlikely to have a large impact on a customer’s future behaviour, and these results bear this out. Methods that deal with sequential data also tend to be much more complex than those dealing with simple nontemporal data, giving an added benefit to expressing the recent information in a non-sequential manner

Data refinement for true concurrency

The majority of modern systems exhibit sophisticated concurrent behaviour, where several system components modify and observe the system state with fine-grained atomicity. Many systems (e.g., multi-core processors, real-time controllers) also exhibit truly concurrent behaviour, where multiple events can occur simultaneously. This paper presents data refinement defined in terms of an interval-based framework, which includes high-level operators that capture non-deterministic expression evaluation. By modifying the type of an interval, our theory may be specialised to cover data refinement of both discrete and continuous systems. We present an interval-based encoding of forward simulation, then prove that our forward simulation rule is sound with respect to our data refinement definition. A number of rules for decomposing forward simulation proofs over both sequential and parallel composition are developed

Net processes correspond to derivation processes in graph grammars

AbstractThe aim of this paper is to compare the running behaviour of Petri nets, given by firing sequences and processes, with derivations and derivation processes in graph grammars. In a first step, Petri nets are simulated by graph grammars so that each firing in a net corresponds exactly to a direct derivation in the simulating graph grammar. In a second step the non-sequential behaviour of nets described by net processes is related to the non-sequential behaviour of graph grammars given by derivation processes. a one-to-one correppondence can be established between the processes on a Petri net and the complete conflict-free processes in the graph grammar simulating the net. This adds a new piece of evidence substantiating the close relationship between net and graph grammar theory

Modeling and removal of optical ghosts in the PROBA-3/ASPIICS externally occulted solar coronagraph

Context: ASPIICS is a novel externally occulted solar coronagraph, which will be launched onboard the PROBA-3 mission of the European Space Agency. The external occulter will be placed on the first satellite approximately 150 m ahead of the second satellite that will carry an optical instrument. During 6 hours per orbit, the satellites will fly in a precise formation, constituting a giant externally occulted coronagraph. Large distance between the external occulter and the primary objective will allow observations of the white-light solar corona starting from extremely low heights 1.1RSun. Aims: To analyze influence of optical ghost images formed inside the telescope and develop an algorithm for their removal. Methods: We implement the optical layout of ASPIICS in Zemax and study the ghost behaviour in sequential and non-sequential regimes. We identify sources of the ghost contributions and analyze their geometrical behaviour. Finally we develop a mathematical model and software to calculate ghost images for any given input image. Results: We show that ghost light can be important in the outer part of the field of view, where the coronal signal is weak, since the energy of bright inner corona is redistributed to the outer corona. However the model allows to remove the ghost contribution. Due to a large distance between the external occulter and the primary objective, the primary objective does not produce a significant ghost. The use of the Lyot spot in ASPIICS is not necessary.Comment: 14 pages, 13 figure

Dynamic Bayesian smooth transition autoregressive models applied to hourly electricity load in southern Brazil

Dynamic Bayesian Smooth Transition Autoregressive (DBSTAR) models are proposed for nonlinear autoregressive time series processes as alternative to both the classical Smooth Transition Autoregressive (STAR) models of Chan and Tong (1986) and the Bayesian Simulation STAR (BSTAR) models of Lopes and Salazar (2005). Unlike those, DBSTAR models are sequential polynomial dynamic analytical models suitable for inherently non-stationary time series with non-linear characteristics such as asymmetric cycles. As they are analytical, they also avoid potential computational problems associated with BSTAR models and allow fast sequential estimation of parameters. Two types of DBSTAR models are defined here based on the method adopted to approximate the transition function of their autoregressive components, namely the Taylor and the B-splines DBSTAR models. A harmonic version of those models, that accounted for the cyclical component explicitly in a flexible yet parsimonious way, were applied to the well-known series of annual Canadian lynx trappings and showed improved fitting when compared to both the classical STAR and the BSTAR models. Another application to a long series of hourly electricity loading in southern Brazil, covering the period of the South-African Football World Cup in June 2010, illustrates the short-term forecasting accuracy of fast computing harmonic DBSTAR models that account for various characteristics such as periodic behaviour (both within-the-day and within-the-week) and average temperature

A Behavioural Transformer for Effective Collaboration between a Robot and a Non-stationary Human

A key challenge in human-robot collaboration is the non-stationarity created by humans due to changes in their behaviour. This alters environmental transitions and hinders human-robot collaboration. We propose a principled meta-learning framework to explore how robots could better predict human behaviour, and thereby deal with issues of non-stationarity. On the basis of this framework, we developed Behaviour-Transform (BeTrans). BeTrans is a conditional transformer that enables a robot agent to adapt quickly to new human agents with non-stationary behaviours, due to its notable performance with sequential data. We trained BeTrans on simulated human agents with different systematic biases in collaborative settings. We used an original customisable environment to show that BeTrans effectively collaborates with simulated human agents and adapts faster to non-stationary simulated human agents than SOTA techniques

On the Model of Computation of Place/Transition Petri Nets

In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical "token game", one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. More precisely, we introduce the new notion of decorated processes of Petri nets and we show that they induce on nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net N can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification